Power-emoting (also known as powergaming) in it's simplest form is the act of any character doing something they'd realistically be unable to do. In truth, even Metagaming is a form of power-emoting. Power-emoting is detrimental to Roleplaying through the breaking of immersion, and a loss for fairness to other players. Power-emoting is most easily displayed when an emote made by a player is made that does not allow another player to respond/defend himself from. This is considered power-emoting because it is giving one's character the ability to overpower someone else's character without any resistance, while realistically there'd be quite some resistance.
An example of power-emoting.
How such an emote should look.
Power-emoting can also be displayed through a character's abilities, or prowess in battle. A character in full plate mail would be unable to perform difficult feats of agility, due to the weight of his armor, and a Halfling would not easily be able to beat an Orc in a challenge of strength. Power-emoting can even extend to magical abilities, as mages likewise have limits to their power, with magical conflicts ironically being the most common source of power-emoting.
To avoid powergaming, one should always ensure they understand the limits and strengths of their own, and other characters. Likewise, an openness to defeat is helpful, as most powergaming offenses are done in an effort to beat another character. If you can't do it in or see it possible in real life, you should not be able to do it in Rp, some cases like magic do not work this way.
NOTE: Just because someone else power-emotes does not mean its okay to power-emote yourself. If someone blatantly power-emotes, PM the person respectfully and refute gently, if they refuse and continue power-emoting than it is either best to let it go, or contact a moderator if it persists.